├── README.md
└── rdf.py


/README.md:
--------------------------------------------------------------------------------
 1 | # Radial Distribution Function
 2 | Radial Distribution Function(rdf) 镜像分布函数计算
 3 | 
 4 | 
 5 | ## 参考
 6 | [[VMD] 径向分布函数求配位数的问题求助@sobereva](http://bbs.keinsci.com/thread-15102-1-1.html)<br>
 7 | [9041 周期性 RDF 计算程序 CryRDF](https://zhuanlan.zhihu.com/p/178610319)<br>
 8 | 
 9 | ## 程序内容解释
10 | [镜像分布函数rdf计算方法和程序](https://cndaqiang.github.io//2020/11/29/rdf/)
11 | 
12 | ## 环境
13 | - python3
14 | - Module: numpy, matplotlib
15 | 
16 | 使用示例
17 | - 查看帮助
18 | ```
19 | (python37) cndaqiang@mac Desktop$ ./rdf.py
20 | Usage: ./rdf.py [ xxx.xyz | xxx.vasp ] [ none | a | a b c]
21 | ```
22 | - 计算晶格常数为30Ang的立方晶胞的rdf
23 | ```
24 | (python37) cndaqiang@mac Desktop$ ./rdf.py 303030.xyz 30
25 | read from 303030.xyz
26 | XYZ: set cell to
27 | a: [30.  0.  0.]
28 | b: [ 0. 30.  0.]
29 | c: [ 0.  0. 30.]
30 | nstep,ntyp,nat 1 ['O' 'H'] [ 884 1768]
31 | Super cell [1. 1. 1.]
32 | ['O-O' 'O-H' 'H-H']
33 | Save rdf to 303030.xyz.O-O.averagerdf.dat
34 | Save rdf to 303030.xyz.O-H.averagerdf.dat
35 | Save rdf to 303030.xyz.H-H.averagerdf.dat
36 | Save png to 303030.xyz.averagerdf.png
37 | ```
38 | - 计算晶格常数`a=3.967 b=8.121 c=8.320`的长方型原胞rdf
39 | ```
40 | (python37) cndaqiang@mac Desktop$ ./rdf.py 123.xyz 3.967 8.121 8.320
41 | read from 123.xyz
42 | XYZ: set cell to
43 | a: [3.967 0.    0.   ]
44 | b: [0.    8.121 0.   ]
45 | c: [0.   0.   8.32]
46 | nstep,ntyp,nat 1 ['O' 'H'] [12 24]
47 | Super cell [3. 1. 1.]
48 | ['O-O' 'O-H' 'H-H']
49 | Save rdf to 123.xyz.O-O.averagerdf.dat
50 | Save rdf to 123.xyz.O-H.averagerdf.dat
51 | Save rdf to 123.xyz.H-H.averagerdf.dat
52 | Save png to 123.xyz.averagerdf.png
53 | ```
54 | - vasp格式
55 | ```
56 | (python37) cndaqiang@mac Desktop$ ./rdf.py 123.vasp
57 | read from 123.vasp
58 | nstep,ntyp,nat 1 ['H' 'O'] [24 12]
59 | Super cell [3. 1. 1.]
60 | ['H-H' 'H-O' 'O-O']
61 | Save rdf to 123.vasp.H-H.averagerdf.dat
62 | Save rdf to 123.vasp.H-O.averagerdf.dat
63 | Save rdf to 123.vasp.O-O.averagerdf.dat
64 | Save png to 123.vasp.averagerdf.png
65 | ```
66 | 
67 | ## 结果展示
68 | ```
69 | (python37) cndaqiang@mac Desktop$ ./rdf.py cubic.xyz 12 12 12
70 | read from cubic.xyz
71 | XYZ: set cell to
72 | a: [12.  0.  0.]
73 | b: [ 0. 12.  0.]
74 | c: [ 0.  0. 12.]
75 | nstep,ntyp,nat 1 ['O' 'H'] [ 61 122]
76 | Super cell [2. 2. 2.]
77 | ['O-O' 'O-H' 'H-H']
78 | Save rdf to cubic.xyz.O-O.averagerdf.dat
79 | Save rdf to cubic.xyz.O-H.averagerdf.dat
80 | Save rdf to cubic.xyz.H-H.averagerdf.dat
81 | Save png to cubic.xyz.averagerdf.png
82 | ```
83 | 与VMD计算结果对比
84 | ![](https://cndaqiang.github.io/uploads/2020/11/vmd.png)
85 | ![](https://cndaqiang.github.io/uploads/2020/11/cubic.xyz.averagerdf.png)
86 | 


--------------------------------------------------------------------------------
/rdf.py:
--------------------------------------------------------------------------------
  1 | #!/usr/bin/env python3
  2 | # -*- coding: utf-8 -*-
  3 | """
  4 | @Time    : 2020-11-29 @IOP
  5 | @Author  : cndaqiang
  6 | @Blog    : cndaqiang.github.io
  7 | @File    : 读入含时xyz或POSCAR处理rdf
  8 | """
  9 | 
 10 | import sys
 11 | import os
 12 | import numpy as np
 13 | 
 14 | #统计的最短最远距离
 15 | minr=0 #1e-15 #avoid rdf/0
 16 | maxr=10.0
 17 | dr=0.1
 18 | #因为rdf:g(r)=dN/(4*pi*dr*r^2*\rho_N), 一般仅在r=a_0时取最大值,此时dr就影响计算结果,dr翻倍就减半, dr越大越小,但是积分不变的
 19 | #
 20 | ngrid=int(np.ceil(maxr-minr)/dr)
 21 | #dr=(maxr-minr)/ngrid
 22 | ngrid=ngrid+2
 23 | grid=np.arange(ngrid)*dr+minr
 24 | 
 25 | #xyz文件时需要
 26 | #xyz格式类型,默认beforenum+1行是总原子数,header+1行开始是原子结构
 27 | #有的程序输出的格式不规范,在这里定义
 28 | beforenum=0 #/3 #beforenum+1行是总原子数
 29 | header=2    #/9 #header+1行开始是原子结构
 30 | #原胞
 31 | cell=np.zeros([3,3])
 32 | cell[0]=np.array([12,0,0]) #a
 33 | cell[1]=np.array([0,12,0]) #b
 34 | cell[2]=np.array([0,0,12]) #c
 35 | 
 36 | #-----Input File
 37 | if len(sys.argv) == 1:
 38 |     print("Usage: "+str(sys.argv[0])+" [ xxx.xyz | xxx.vasp ] [ none | a | a b c]")
 39 |     exit()
 40 | if len(sys.argv) > 1:
 41 |     inputfile = str(sys.argv[1])
 42 | else:
 43 |     inputfile = "./292.xyz"
 44 | if os.path.exists(inputfile):
 45 |     print("read from",inputfile)
 46 | else:
 47 |     print("EXIT: There are not "+inputfile)
 48 |     exit()
 49 | if len(sys.argv) == 3:  # 只输入一个晶格参数,视为cubic
 50 |     cell[:,:]=0
 51 |     for i in np.arange(3): cell[i,i]=float(sys.argv[2])
 52 | if len(sys.argv) == 5: #输入三个晶格参数,视为长方形 a b  c晶胞
 53 |     cell[:,:]=0
 54 |     for i in np.arange(3): cell[i,i]=float(sys.argv[2+i])
 55 | 
 56 | #-----
 57 | 
 58 | 
 59 | #----
 60 | def readxyz(xyzfile):
 61 |     f=open(xyzfile,'r')
 62 |     for i in np.arange(beforenum): f.readline()#原子数前有几行
 63 |     natoms=int(f.readline())#原子数
 64 |     ierror=f.seek(0,0)
 65 |     rownum=len(f.readlines())#总行数
 66 |     if rownum%(natoms+header) == 0:
 67 |         nstep=int(rownum/(natoms+header))  #每个xyz单元,2个
 68 |     else:
 69 |         print("rownum can't be split by natoms + header",rownum,natoms+header)
 70 |         nstep=int(rownum/(natoms+header))  #每个xyz单元,2个
 71 |     #nstep=2 也可以在这里限制总的nstep步数
 72 |     #收集元素种类和数量
 73 |     ntyp=np.array([]).astype(np.str)
 74 |     nat=np.array([])
 75 |     ierror=f.seek(0,0)
 76 |     for i in np.arange(header): f.readline()
 77 |     for i in np.arange(natoms):
 78 |         label=f.readline().split()[0]
 79 |         if np.where(ntyp==label)[0].size == 0:
 80 |            ntyp =   np.append(ntyp,label)
 81 |            nat  =   np.append(nat,1)
 82 |         else:
 83 |             nat[np.where(ntyp==label)[0][0]]=nat[np.where(ntyp==label)[0][0]]+1
 84 |     nat=nat.astype(np.int)
 85 |     #按照原子数排序,画图的顺序和中心原子
 86 |     ntyp=ntyp[np.argsort(nat)]
 87 |     nat=nat[np.argsort(nat)]
 88 | 
 89 |     natmax=int(np.max(nat))
 90 |     totaltype=ntyp.size
 91 |     #======
 92 |     xyz=np.zeros([nstep,totaltype,natmax,3]) #步数,元素,原子编号,xyz
 93 |     ierror=f.seek(0,0)
 94 |     for istep in np.arange(nstep):
 95 |         index=np.zeros(totaltype)
 96 |         for i in np.arange(header): f.readline()
 97 |         for iatom in np.arange(natoms):
 98 |             line=f.readline()
 99 |             label=line.split()[0]
100 |             itype=np.where(ntyp==label)[0][0]
101 |             for idir in np.arange(3):
102 |                 xyz[istep,itype,int(index[itype]),idir]=float(line.split()[idir+1])
103 |             index[itype]=index[itype]+1
104 |     f.close()
105 |     return nstep,ntyp,nat,xyz
106 | def readposcar(poscar):
107 |     f=open(poscar,'r')
108 |     f.readline()
109 |     alat=np.float(f.readline().split()[0])
110 |     cell=np.zeros([3,3])
111 |     for i in np.arange(3):
112 |         cell[i,0:3] = [ float(x) for x in f.readline().split()[0:3] ] 
113 |     cell=cell*alat
114 |     #
115 |     nstep=1
116 |     #元素
117 |     ntyp=np.array(f.readline().split())
118 |     nat=np.array(f.readline().split())
119 |     totaltype=min(ntyp.size,nat.size)
120 |     ntyp=ntyp[0:totaltype].copy()
121 |     nat=nat[0:totaltype].copy().astype(np.int)
122 |     #坐标类型
123 |     xyztype=f.readline().split()[0]
124 |     #读坐标
125 |     natmax=int(np.max(nat))
126 |     #坐标
127 |     xyz=np.zeros([nstep,totaltype,natmax,3])
128 |     for istep in np.arange(nstep):
129 |         for itype in np.arange(totaltype):
130 |             for i in np.arange(nat[itype]):
131 |                 xyz[istep,itype,i,0:3]=[ float(x) for x in f.readline().split()[0:3] ] 
132 |                 #
133 |                 #    xyz[istep,itype,i,0:3]=[ (xyz[istep,itype,i,0:3]*cell[:,d]).sum() for d in np.arange(3) ]
134 | 
135 | 
136 |     #计算坐标
137 |     if xyztype[0] == 'D' or xyztype[0] == 'd':
138 |         Dxyz=xyz.copy()
139 |         for d in np.arange(3):
140 |             xyz[:,:,:,d]=(Dxyz*cell[:,d]).sum(axis=3)
141 |         #for d in np.arange(3):
142 |         #    xyz=xyz[:,:,:,0:3]*cell[0:3,d]
143 |     else:
144 |         xyz=xyz*alat
145 |     return nstep,ntyp,nat,xyz,cell
146 | 
147 | def move2cell(nstep,ntyp,nat,xyz,cell):
148 |     for istep in np.arange(nstep):
149 |         for i in np.arange(ntyp.size):
150 |             for j in np.arange(nat[i]):
151 |                 #下面这套算法不是严格的，暂时没有好的方法
152 |                 while xyz[istep,i,j,0] > cell[0,0]:
153 |                     #print("i,j",i,j,"addcell 0")
154 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]-cell[0,:]
155 |                 while xyz[istep,i,j,0] < 0:
156 |                     #print("i,j",i,j,"delcell 0")
157 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]+cell[0,:]
158 |                 while xyz[istep,i,j,1] > cell[1,1]:
159 |                     #print("i,j",i,j,"addcell 1")
160 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]-cell[1,:]
161 |                 while xyz[istep,i,j,1] < 0:
162 |                     #print("i,j",i,j,"delcell 1")
163 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]+cell[1,:]
164 |                 while xyz[istep,i,j,2] > cell[2,2]:
165 |                     #print("i,j",i,j,"addcell 2")
166 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]-cell[2,:]
167 |                 while xyz[istep,i,j,2] < 0:
168 |                     #print("i,j",i,j,"delcell 2")
169 |                     xyz[istep,i,j,:]=xyz[istep,i,j,:]+cell[2,:] 
170 | def calV(cell):
171 |     V=0
172 |     V=V+(cell[0,1]*cell[1,2]-cell[0,2]*cell[1,1])*cell[2,0] 
173 |     V=V+(cell[0,2]*cell[1,0]-cell[0,0]*cell[1,2])*cell[2,1]
174 |     V=V+(cell[0,0]*cell[1,1]-cell[0,1]*cell[1,0])*cell[2,2]
175 |     return V
176 | 
177 | 
178 | def savedata(A,B,filename):
179 |     f=open(filename,'w')
180 |     for i in np.arange(A.size):
181 |         f.write(str(A[i])+"\t"+str(B[i])+'\n')
182 |     f.close()
183 | #
184 | 
185 | def calrdf(A_in,B_in):
186 |     A=A_in.copy()
187 |     B=B_in.copy()
188 |     rdf=np.zeros(ngrid)
189 |     for i in np.arange(A.shape[0]):
190 |         dis=np.sqrt(np.square(B-A[i]).sum(axis=1))
191 |         choose=np.floor(  ( dis[(dis >= max(minr, 1e-5) )&(dis < maxr+10*dr )] - minr )/dr  ).astype(int)
192 |         #忽略本身原子
193 |         #向下取整,处以体积4/3pi(r^3 -(r-dr)^3)
194 |         choose=choose[choose<ngrid]
195 |         for uniq in np.unique(choose):
196 |             rdf[uniq]=rdf[uniq]+choose[(choose==uniq)].size
197 |     return rdf*1.0/A.shape[0] #算一个A原子就够了,算多个A原子进行平均
198 | def rdf(nstep,ntyp,nat,xyz,cell):
199 |     rdftype=int(np.arange(ntyp.size+1).sum())#几种rdf
200 |     timerdf=np.zeros([nstep,rdftype,ngrid])#含时rdf
201 |     rdflable=np.zeros(rdftype)#rdftype种键长
202 |     rdflable=rdflable.astype(np.str)
203 |     irdftype=0
204 |     supercell=np.zeros(3)
205 |     for i in np.arange(3):  supercell[i]=max(np.around(maxr/cell[i,i]),2) #超胞数量，至少3x3x3
206 |     supercell.astype(np.int)
207 |     print("Super cell",supercell)
208 |     for istep in np.arange(nstep):
209 |         for left in np.arange(ntyp.size):
210 |             lindex=left#A元素编号
211 |             A=xyz[istep,lindex,0:nat[lindex]].copy()#原胞中的A
212 |             for right in np.arange(ntyp.size-left):
213 |                 rindex=lindex+right#B元素编号
214 |                 rdflable[irdftype]=ntyp[lindex]+"-"+ntyp[rindex]
215 |                 #下面计算AB两种原子的rdf
216 |                 for x in np.arange(-supercell[0],1+supercell[0]):
217 |                     for y in np.arange(-supercell[1],1+supercell[1]):
218 |                         for z in np.arange(-supercell[2],1+supercell[2]):
219 |                             B=xyz[istep,rindex,0:nat[rindex],:]+x*cell[0]+y*cell[1]+z*cell[2]#超胞中的B
220 |                             timerdf[istep,irdftype,0:ngrid] = timerdf[istep,irdftype,0:ngrid] + calrdf(A,B)
221 |                 rho=1.0*nat[rindex]/calV(cell)
222 |                 timerdf[istep,irdftype,0:ngrid]=timerdf[istep,irdftype,0:ngrid]/(rho*4.0/3.0*np.pi*dr*(3*grid[:]**2+3*grid[:]*dr+dr**2)) #dN/(4*pi*rho_N,r^2*dr)
223 |                 #这里使用体积4/3*pi[ (r+dr)^3-r^3 ]=4/3*pi[ dr^3 +3r^2dr+3r*dr^2]
224 |                 irdftype=irdftype+1
225 |     print(rdflable)
226 |     return rdftype,rdflable,timerdf #种类数,标签,数据timerdf[istep,irdftype,igrid]
227 | 
228 | if inputfile[-3:] == 'xyz':
229 |     nstep,ntyp,nat,xyz=readxyz(inputfile)
230 |     cell=cell.copy()#使用输入的cell
231 |     print("XYZ: set cell to ")
232 |     print('a:',cell[0])
233 |     print('b:',cell[1])
234 |     print('c:',cell[2])
235 | else: #POSCAR
236 |     del cell#删除为xyz设置的cell
237 |     nstep,ntyp,nat,xyz,cell=readposcar(inputfile)
238 | 
239 | #move to unit cell
240 | move2cell(nstep,ntyp,nat,xyz,cell)
241 | print("nstep,ntyp,nat",nstep,ntyp,nat)
242 | 
243 | rdftype,rdflable,timerdf=rdf(nstep,ntyp,nat,xyz,cell)
244 | 
245 | avTrdf=timerdf.mean(axis=0)
246 | 
247 | 
248 | #保存数据
249 | for irdftype in np.arange(rdftype):
250 |     rdffile=inputfile+"."+rdflable[irdftype]+'.averagerdf.dat'
251 |     print('Save rdf to '+rdffile)
252 |     savedata(np.around(grid,3),np.around(avTrdf[irdftype],6),rdffile)#分别保留3,5位有效数字
253 | 
254 | if False: #输出到屏幕
255 |     for istep in np.arange(nstep):
256 |         print("r,\t",rdflable,"\t,rdf")
257 |         for igrid in np.arange(ngrid):#跳过初始的0
258 |             print(np.around(grid[igrid],2),"\t",np.around(timerdf[istep,:,igrid],2))
259 | 
260 | #下面为画图脚本
261 | 
262 | if True: #画图
263 |     from matplotlib import pyplot as plt
264 |     #
265 |     row=max(int(1.0*rdftype/np.sqrt(rdftype)),2) #向下取整
266 |     col=max(int(np.ceil(rdftype/row)),2)
267 |     fig, axs = plt.subplots(row,col,sharex=True,sharey=False,figsize=(8*col,8*row))
268 |     i=0
269 |     for x in np.arange(row):
270 |         for y in np.arange(col):
271 |             if i  < rdftype:#画单个键长
272 |                 axs[x,y].plot(grid,avTrdf[i],label=rdflable[i])
273 |                 axs[x,y].hlines(1.0, minr,maxr)
274 |                 axs[x,y].legend()
275 |                 i=i+1
276 |             elif i  == rdftype :#如果还有空间就画所有键长
277 |                 for j in np.arange(rdftype):
278 |                     axs[x,y].plot(grid,avTrdf[j],label=rdflable[j])
279 |                     axs[x,y].hlines(1.0, minr,maxr)
280 |                     axs[x,y].legend()
281 |                     i=i+1
282 |                 break
283 |             else: 
284 |                 break            
285 |     plt.xlim(minr,maxr)
286 |     plt.ylim(0,None)
287 |     #plt.set_ylim(0,None)
288 |     
289 |     filename=inputfile+'.averagerdf.png'
290 |     print('Save png to '+filename)
291 |     plt.savefig(filename,dpi=100)


--------------------------------------------------------------------------------